Finite Group Databasebeta

← #26136923

Subgroups — #26136923

Order 12032.

294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q32×D47C211yesmaximal, characteristic, complemented
2C2×#15688962C211yesmaximal, characteristic, complemented
3C2×#15688960C211yesmaximal, characteristic, complemented
4#20245475C211yesmaximal, characteristic
5#20241568C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C32C211yesmaximal, characteristic, complemented
7C47×#1416C211yesmaximal, characteristic, complemented
8C2×Q16×D47—21no—
9C2×Dic376C2211yescharacteristic
10C2×#13093970—21no—
11Q32×D47—22no—
12Q32×D47—22no—
13C2×D752C2211yescharacteristic
14C2×C16×D47C2211yescharacteristic
15#15689360—21no—
16#15688962—22no—
17#15688960—22no—
18C2×C47⋊C32C2211yescharacteristic
19#15688923—21no—
20C2×Q32×C47C2211yescharacteristic
21C2×C32×C47C2211yescharacteristic
22C47×#366C2211yescharacteristic
23C2×Q8×D47—41no—
24C2×Dic188—21no—
25C2×#10625337—41no—
26Q16×D47—24no—
27Q16×D47—42no—
28C2×D376—21no—
29C2×C8×D47D411yescharacteristic
30#13093999—41no—
31Dic376—21no—
32Dic376D412yescomplemented
33#13093970—24no—
34D752—21no—
35D752—21no—
36C2×C47⋊C16D411yescharacteristic
37C16×D47—21no—
38C16×D47—21no—
39#13093944—41no—
40C47⋊C32—21no—
41C2×Q16×C47—21no—
42Q32×C47—21no—
43Q32×C47D412yescomplemented
44C2×C16×C47C2311yescharacteristic
45#107×C47—21no—
46C32×C47—21no—
47C2×Q8×C47—41no—
48Q8×D47—44no—
49Q8×D47—82no—
50C2×D188—41no—
51C2×D188—81no—
52C2×C4×D47—81no—
53C2×C4×D47D811yescharacteristic
54C2×Dic94—41no—
55C2×Dic94—81no—
56Q16×C47—22no—
57Q16×C47—41no—
58C2×C8×C47C2×D411yescharacteristic
59C4⋊C4×C47—41no—
60#10625337—44no—
61(C2×D47)⋊C4—81no—
62C2×C47⋊C8D811yescharacteristic
63Dic188—22no—
64Dic188—41no—
65D376—41no—
66D376—41no—
67C8×D47—21no—
68C8×D47—21no—
69C16×C47C2×D411yescharacteristic
70C16×C47C2×D411yescharacteristic
71C47⋊C16—21no—
72C22×D47—81no—
73C22×D47D1611yescharacteristic
74Q8×C47—42no—
75Q8×C47—81no—
76C2×C4×C47—81no—
77C2×C4×C47—81no—
78C2×C4×C47C2×D811yescharacteristic
79C2×Dic47—81no—
80C2×Dic47D1611yescharacteristic
81D188—81no—
82D188—81no—
83D188—162no—
84C4×D47—21no—
85C4×D47—21no—
86C4×D47—84no—
87Dic94—42no—
88Dic94—84no—
89Dic94—81no—
90C8×C47#12011yescharacteristic
91C8×C47AGL(1,ℤ/8)11yescharacteristic
92C47⋊C8—21no—
93#13662—471nomaximal, Sylow
94C22×C47C2×D1611yescharacteristic
95C2×D47—21no—
96C2×D47—21no—
97C2×D47—161no—
98C2×D47—161no—
99C2×D47—161no—
100C2×D47SD6412yescomplemented
101C4×C47—82no—
102C4×C47—161no—
103C4×C47#44711yescharacteristic
104C4×C47#50911yescharacteristic
105Dic47—21no—
106Dic47—82no—
107C22×Q32—471no—
108C2×SD64—471no—
109C2×SD64—471no—
110#2215—471no—
111#1416—471no—
112#1416D4711yescharacteristic, complemented
113C22⋊C32—471no—
114C2×C47#218411yescharacteristic
115C2×C47C2×SD6411yescharacteristic
116C2×C47#226411yescharacteristic
117D47—22no—
118D47—321no—
119C22×Q16—941no—
120C2×Q32—471no—
121C2×Q32—941no—
122C2×Q32—942no—
123C2×Q32—942no—
124C2×Q32C2×D4711yescharacteristic
125C2×D16—471no—
126C22×C16—471no—
127#466—941no—
128SD64—942no—
129SD64—942no—
130C2×C32—471no—
131C2×C32C2×D4711yescharacteristic
132#366C2×D4711yescharacteristic
133#357—941no—
134C47#1366211yescharacteristic, complemented, Sylow
135C22×Q8—1881no—
136C2×Q16—21no—
137C2×Q16—944no—
138C2×Q16—941no—
139C2×Q16—1881no—
140C2×Q16—1882no—
141C2×D8—941no—
142C22×C8—471no—
143#121—1881no—
144Q32—21no—
145Q32—472no—
146Q32—944no—
147Q32—941no—
148Q32D18812yescomplemented
149D16—941no—
150D16—941no—
151C2×C16—471no—
152C2×C16—941no—
153C2×C16—941no—
154C2×C16C22×D4711yescharacteristic
155#107—21no—
156#102—1881no—
157C32—21no—
158C32—941no—
159C2×Q8—41no—
160C2×Q8—3761no—
161C2×Q8—3762no—
162C2×Q8—1884no—
163C2×Q8—1881no—
164C2×D4—3761no—
165C2×D4—1881no—
166C22×C4—471no—
167C22×C4—3761no—
168Q16—22no—
169Q16—41no—
170Q16—942no—
171Q16—1884no—
172Q16—1881no—
173D8—1881no—
174D8—1881no—
175C2×C8—471no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8D4×D4711yescharacteristic
179C4⋊C4—41no—
180C22⋊C4—3761no—
181C16—941no—
182C16C2×D18811yescharacteristic
183C16D4×D4711yescharacteristic
184C23—471no—
185C23—3761no—
186Q8—42no—
187Q8—81no—
188Q8—3764no—
189Q8—3761no—
190Q8—1882no—
191D4—3761no—
192D4—3761no—
193D4—7522no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—471no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—3764no—
200C2×C4—3761no—
201C2×C4D8×D4711yescharacteristic
202C8—941no—
203C8#1309399411yescharacteristic
204C8#1309405111yescharacteristic
205C22—472no—
206C22—941no—
207C22—941no—
208C22—7521no—
209C22—7521no—
210C22—7521no—
211C22D16×D4711yescharacteristic
212C4—82no—
213C4—161no—
214C4—941no—
215C4—3762no—
216C4#1568925811yescharacteristic
217C4#1568956011yescharacteristic
218C2—942no—
219C2—15041no—
220C2#2024530111yescharacteristic
221C2SD64×D4711yescharacteristic
222C2#2024570711yescharacteristic
subgroupG/H
centerC22D16×D47
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1416C2
socleC22×C47C2×D16
prime radical#20245475C2
hypercenter#1416D47
hypocenterC47#13662
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×Q32×D47C2semidirect
2. C2×#15688962C2semidirect
3. C2×#15688960C2semidirect
5. #20241568C2semidirect
6. (C2×D47)⋊C32C2semidirect
7. C47×#1416C2semidirect
32. Dic376D4semidirect
43. Q32×C47D4semidirect
100. C2×D47SD64semidirect
112. #1416D47semidirect
134. C47#13662semidirect
148. Q32D188semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q32×D472
C2×#156889622
C2×#156889602
#202454752
#202415682
(C2×D47)⋊C322
C47×#14162
#1366247